The reflexive property of equality states that every value equals itself.
General Example: a = a
Practical Example: 5 = 5

The symmetry property of equality states that if a first value equals a second value, then the second must be equal to the first.
General Example: If a = b, then b = a.
Practical Example: If (3 + 4) = 7, then 7 = (3 + 4).

The transitive property of equality states that if a first value equals a second value, and the second value equals a third value, then
the first value is equal to the third value.
General Example: If a = b, and b = c, then a = c.
Practical Example: If (2 + 3) = 5, and 5 = (10 - 5), then (2+3) = (10 - 5).

The substitution property of equality states that if a first value is equal to a second value, but they are written in different forms, then
one value may be substituted for the other.
General Example: If a = b, then a may be substituted for b, and conversely.
Practical Example: If (2+3) = 5, then 5 may be substituted for (2+3), or (2+3) may be substituted for 5.
Note: The values must be written in different forms, otherwise there is no need for a substitution.

The addition property of equality states that if a first value is equal to a second value, then the sum of the first value and a third value
is equal to the sum of the second and third values.
General Example: If a = b, then (a + c) = (b + c).
Practical Example: If x = 5, then x + 3 = 5 + 3.

The subtraction property of equality states that if a first value is equal to a second value, then the difference of the first value and a
third value is equal to the difference of the second and third values.
General Example: If a = b, then (a - c) = (b - c).
Practical Example: If 9 = (6 + 3), then 9 - 4 = (6 + 3) - 4.

The multiplication property of equality states that if a first value is equal to a second value, then the product of the first value and a
third value is equal to the product of the second and third values.
General Example: If a = b, then (a · c) = (b · c).
Practical Example: If x = 6, then x · 2 = 6 · 2.

The division property of equality states that if a first value is equal to a second value, then the quotient of the first value and a
third value is equal to the quotient of the second and third values.
General Example: If a = b, then (a / c) = (b / c).
Practical Example: If 12 = (6 + 6), then 12 / 3 = (6 + 6) / 3.